# Fine energy splitting of overlapping Andreev bound states in multi-terminal superconducting nanostructures

## TL;DR

This paper analyzes the energy splitting of overlapping Andreev bound states in multi-terminal superconducting nanostructures, revealing a small reduction factor that enables quantum control of quasiparticles.

## Contribution

It provides a detailed analysis of energy splitting in overlapping Andreev bound states and proposes a scheme for their quantum manipulation.

## Key findings

- Energy splitting is reduced by a factor of √(RG_Q).
- Overlapping Andreev bound states can be quantum manipulated.
- The analysis aids experimental design of multi-terminal superconducting devices.

## Abstract

The recent proposals of experiments with single Andreev bound states make relevant a detailed analysis of these states in multi-terminal superconducting nanostructures. We evaluate the energy splitting of degenerate Andreev bound states, that overlap in a superconducting lead, and find that the splitting is reduced in comparison with their energy by a small factor $\sqrt{R G_Q}$, $R G_Q$ being the dimensionless resistance of the overlap region in the normal state. This permits quantum manipulation of the quasiparticles in these states. We provide a simple scheme of such manipulation.